The band announced on Saturday (local time) that Jagger was told by doctors "he cannot go on tour at this time."
The band added that Jagger "is expected to make a complete recovery so that he can get back on stage as soon as possible."
No more details about 75-year-old Jagger's condition were provided.
The Stones' No Filter Tour was expected to start April 20 in Miami. Other stops included Jacksonville, Florida; Houston; the New Orleans Jazz Festival; Pasadena and Santa Clara in California; Seattle; Denver; Washington, D.C.; Philadelphia; Foxborough, Massachusetts; East Rutherford, New Jersey; Chicago; and Ontario, Canada.
"I really hate letting you down like this," Jagger tweeted Saturday. "I'm devastated for having to postpone the tour but I will be working very hard to be back on stage as soon as I can."
Tour promoters AEG Presents and Concerts West advise ticketholders to hold on to their existing tickets because will be valid for the rescheduled dates.